Device and method for image reconstruction at different x-ray energies, and device and method for x-ray three-dimensional measurement

ABSTRACT

The present invention provides a device and a method for image reconstruction at different X-ray energies that make it possible to achieve image reconstruction with higher accuracy. A device for image reconstruction at different X-ray energies includes: an X-ray source  1  that irradiates a specimen to be imaged  2  with X-rays; an energy-dispersive detector  4  that detects a characteristic X-ray emitted from the specimen to be imaged  2 ; a signal processing means that quantifies the peak of the characteristic X-ray detected by the detector  4 ; and an image reconstruction means that reconstructs an image on the basis of a signal from the signal processing means.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.14/894,325, filed Nov. 25, 2015, which is a National Phase applicationunder 35 U.S.C. §371 of PCT Application No. PCT/JP2014/064330, filed May29, 2014, which claims priority to Japanese Patent Application No.2013-113498, filed May 29, 2013, all of which are hereby incorporated byreference.

TECHNICAL FIELD

The present invention relates to a device and a method for imagereconstruction at different X-ray energies, and a device and a methodfor X-ray three-dimensional measurement.

BACKGROUND ART

An X-ray computed tomography (“CT”) device is capable of obtaining athree-dimensional image including an internal structure of an object bycarrying out reconstruction processing on the images of the object takenwith X-rays from various directions. Hitherto, the features of the X-rayCT device have been used to observe minute internal defects, such as avoid and a crack, in a metal part or a resin part or the like, tomeasure the complicated internal shape of an electronic part, and toanalyze a cause of a failure. See Patent Documents 1 to 4, below.)

With the recent advance of digital technologies, an attempt to use anX-ray CT device as the core of a digital engineering system has begun.The digital engineering system represents the technology for integratinga sophisticated computer-assisted design (“CAD”)/computer-assistedmodeling (“CAM”) system, a three-dimensional formative system, and athree-dimensional measurement system to achieve efficiency and highquality throughout the whole process from development to manufacture.Combining these technologies makes it possible to repeatedly design andmake prototypes without making molds and to commercialize products in ashort time and at low cost. A reduced risk in development is expected bysharing accurate and complete production and technological data.

As a three-dimensional measurement system, a digitizer, a light-sectionmethod and the like have been proposed. However, it is extremelydifficult to measure the internal shape of an object to be measured bythe foregoing methods although the methods permit accurate measurementof surface shapes. In contrast to the measurement methods, there hasbeen proposed an ultrasonic diagnosis that is capable of determining thepresence of an internal space. However, it is also difficult toaccurately grasp an internal shape by the ultrasonic diagnosis. Forthese reasons, an X-ray CT device is expected as the onlythree-dimensional measurement system capable of also determining aninternal structure.

CITATION LIST Patent Document

Patent Document 1: JP2006-125960A

Patent Document 2: JP2006-329917A

Patent Document 3: JP2008-70219A

Patent Document 4: JPH11-281747A

SUMMARY Technical Problem

How to improve the accuracy of measurement of CT data is a crucialfactor in using an X-ray CT device as a three-dimensional measurementsystem. In the case of a CT image, an artifact, a noise, a blur or thelike occurs depending on measurement conditions or in a reconstructionprocess, resulting in dimensional differences between an actual specimenand an obtained image. An artifact is caused by, for example, aconsiderable difference in absorption rate in the case where metals arescattered in a resin, or in the case where the X-ray transmissiondistance significantly varies according to an imaging direction. One ofthe causes for the dimensional difference between the specimen and theimage attributable to such an artifact or the like is that theconventional CT image reconstruction method does not give considerationto a mass attenuation coefficient (=linear attenuation coefficient) μ,which differs for each composition contained in a specimen.

An X-ray that has passed through a material attenuates due to theinteractions with the material, typically represented by photoelectricabsorption, Compton scattering, and electron pair creation. When anX-ray having a single energy level passes through a material having athickness t, a relationship represented by the following expressionholds between an incident X-ray intensity (=the number of incidentphotons) I₀ and a transmitted X-ray intensity I:

I=I ₀exp(−μt)  (1)

Expression (1) holds for imaging with a monochromatic X-ray. However, inthe case of a continuous X-ray used for actual measurement, expression(1) does not hold, because the mass attenuation coefficient changesaccording to the energy of an incident X-ray. For the continuous X-ray,the transmitted X-ray intensity I is represented by the integrationsystem of energy indicated by expression (2) given below.

I=∫I ₀(E)exp(−μ(E)t)dE  (2)

To accurately reconstruct an image, expression (2) should be used forthe calculation. However, because of the problems with the performanceof a detector and the amount of calculation, a currently used X-ray CTdevice assumes that the continuous X-ray is a monochromatic X-ray andcarries out the calculation for reconstruction.

Means for meeting such a challenge include a method using amonochromatic X-ray and a dual energy scanning method, in which data isgathered at different tube voltages. However, the irradiation dose ofthe monochromatic X-ray inconveniently decreases due to themonochromatization, thus limiting its use to specific facilities where asufficient dose of radiation can be obtained. Further, the dual energyscanning method requires a plurality of times of imaging at differenttube voltages, leaving some challenges to be met, such as positionaldeviations and prolonged measurement time.

Further, a conventional X-ray CT device for three-dimensionalmeasurement is known to be incapable of maintaining dimensional accuracyin the measurement of an actual object to be measured whereas it iscapable of maintaining a certain level of dimensional accuracy when aparticular measurement standard, e.g. a calibration jig, is used. Thisis because, for example, the resolution of an X-ray detector is lowerthan the actual measurement accuracy, or the shapes and the materials ofan actual object to be measured vary. Hence, there has been a demand fordeveloping a technique for correcting images acquired by an X-ray CTdevice.

An object of the present invention is to provide a device and a methodfor image reconstruction at different X-ray energies and a device and amethod for X-ray three-dimensional measurement that make it possible toachieve highly accurate image reconstruction by removing an artifact orthe like, which has hitherto been a problem, by correction.

Solution to Problem

To this end, provided is a device for image reconstruction at differentX-ray energies, including, for example: an X-ray source that irradiatesa specimen to be imaged with X-rays; an energy-dispersive detector thatdetects a characteristic X-ray emitted from the specimen to be imaged; asignal processor that quantifies the peak of the characteristic X-raydetected by the detector; and an image reconstruction device thatreconstructs an image on the basis of a signal from the signalprocessor.

Further, provided is a method for image reconstruction at differentX-ray energies including the steps of: irradiating a specimen to beimaged with X-rays; detecting a characteristic X-ray emitted from thespecimen to be imaged by an energy-dispersive detector; quantifying thepeak of the detected characteristic X-ray; and reconstructing an imageon the basis of quantified data of the characteristic X-ray peak.

Further, provided is an X-ray three-dimensional measurement deviceincluding: an image acquisition device that acquires an X-ray CT imageof an object to be measured on a three-dimensional coordinate axis; anactual measurement device that actually measures a three-dimensionalshape of the object to be measured on the three-dimensional coordinateaxis; and an image correction device that corrects the X-ray CT imagesuch that a sinogram of the X-ray CT image of the object to be measuredwhich has been acquired by the image acquisition device converges to asinogram of a three-dimensional shape of the object to be measured whichhas been actually measured by the actual measurement device.

Further, provided is an X-ray three-dimensional measurement methodincluding: an image acquisition step of acquiring an X-ray CT image ofan object to be measured on a three-dimensional coordinate axis; anactual measurement step of actually measuring a three-dimensional shapeof the object to be measured on the three-dimensional coordinate axis;and an image correction step of correcting the X-ray CT image such thata sinogram of the X-ray CT image of the object to be measured which hasbeen acquired in the image acquisition step converges to a sinogram of athree-dimensional shape of the object to be measured which has beenactually measured in the actual measurement step.

Further, provided is an X-ray three-dimensional image correction programfor causing a computer to carry out an image correction step ofcorrecting an X-ray CT image such that a sinogram of the X-ray CT imageof an object to be measured which has been acquired on athree-dimensional coordinate axis converges to a sinogram of thethree-dimensional shape of the object to be measured which has beenactually measured on the three-dimensional coordinate axis.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A and FIG. 1B are a side view and a plan view, respectively, of adevice for image reconstruction at different X-ray energies.

FIG. 2 is a diagram for explaining the image reconstruction at differentX-ray energies.

FIG. 3A and FIG. 3B are front views illustrating examples of a detector.

FIG. 4 is a diagram illustrating an example of a characteristic X-ray.

FIG. 5 is a diagram for explaining a dual energy method.

FIG. 6 is a diagram illustrating an example of a linear attenuationcurve.

FIG. 7 is a diagram for explaining a sequential approximatereconstruction method.

FIG. 8A is a sectional view illustrating another example of thedetector, and FIG. 8B is a front view illustrating yet another exampleof the detector.

FIG. 9A and FIG. 9B are a front view and a sectional view, respectively,of still another example of the detector.

FIG. 10 is a diagram for explaining the sorting of energies by a filterin the example illustrated in FIG. 9.

FIG. 11 is a block diagram for explaining the functional configurationof an X-ray three-dimensional measurement device.

FIG. 12 is a side view of the X-ray three-dimensional measurementdevice.

FIG. 13 is a plan view of the X-ray three-dimensional measurementdevice.

FIG. 14 presents diagrams for explaining the sinograms of an X-ray CTimage of an object to be measured.

FIG. 15 presents diagrams for explaining the sinograms of the actualmeasurement data of the three-dimensional shape of an object to bemeasured.

FIG. 16 presents diagram for explaining a maximum likelihood estimationand expectation-maximization reconstruction method.

FIG. 17 presents diagrams illustrating the results of comparison betweena section image reconstructed using the maximum likelihood estimationand expectation-maximization reconstruction method and a section imagereconstructed using a filtered backprojection method.

FIG. 18 presents diagrams for explaining a method for correcting anX-ray CT image by using the sinogram of the actual measurement data of athree-dimensional shape.

FIG. 19 is a flowchart illustrating the X-ray three-dimensionalmeasurement method.

FIG. 20 presents explanatory diagrams illustrating an example in whichthe correction of an X-ray CT image by using sinograms is applied to theimage reconstruction at different X-ray energies.

DESCRIPTION OF EMBODIMENTS

<Device and Method for Image Reconstruction at Different X-Ray Energies>

The FIGS. 1A and 1B are diagrams illustrating an example of theconfiguration of a device for image reconstruction at different X-rayenergies. FIG. 2 is a diagram for explaining specific imagereconstruction at different X-ray energies by the device.

It is desirable to identify the types of materials contained in aspecimen to be imaged 2, in addition to a change in the amount oftransmission used in normal X-ray CT imaging. In order to identify thetypes of materials, characteristic X-rays emitted when irradiating aspecimen 2 with the X-rays from an X-ray source 1 are detected by anenergy-dispersive detector 4, and the information of the elementsconstituting the specimen to be imaged 2 and the concentrations of theelements is acquired from the energy peaks of the characteristic X-rays.

The detector 4 having energy dispersion power may include a plurality ofsub-detectors 40 arranged in a line or panel formation, as illustratedin FIGS. 3A and 3B. The sub-detectors 40 are desirably configured tohave a construction for preventing the influences of scattered rays byshielding the sub-detectors 40 against each other with a shieldingmaterial, such as a lead or tungsten material. Preferably, each of thesub-detectors 40 is capable of acquiring the characteristic X-ray fromeach element obtained when the specimen to be imaged 2, which iscomposed of a plurality of elements, is irradiated with X-rays as aradiation energy spectrum by photon counting. Such a detector may be asemiconductor detector of cadmium telluride (CdTe), zinc cadmium sulfidetelluride (CdZnTe) or the like, or a scintillation detector of cesiumiodide (CsI), sodium iodide (NaI) or the like.

If the sub-detectors 40 are arranged in the line formation (FIG. 3A),then only one section of the specimen 2 disposed between the X-raysource 1 and the detector 4 is imaged while rotating the specimen 2,which is disposed between the X-ray source 1 and the detector 4, by adrive mechanism 3. Each time one section is imaged, the stage of thespecimen is physically moved up or down to stack the tomograms therebyto acquire a three-dimensional image. The drive mechanism 3 is capableof rotating the stage on which the specimen 2 is placed by 360 degreesand translationally moving the stage in an X direction, in which theX-ray source 1 and the detector 4 are connected, in a Y directionorthogonal to the X direction, and in a vertical Z direction.

If the sub-detectors 40 are arranged in the panel formation (FIG. 3B),then a transparent image is acquired while rotating the specimen 2 bythe drive mechanism 3, and then a three-dimensional image is acquired byreconstruction calculation. When the transparent image is acquired foreach rotational angle of the specimen 2, the characteristic X-rayspectrum data for each pixel is acquired at the same time.

If the specimen 2 contains a plurality of materials, then a radiationenergy spectrum having peaks corresponding to the types of elements willbe obtained. The example illustrated in FIG. 4 indicates a spectrumhaving the peaks corresponding to aluminum (Al) and iron (Fe).

FIG. 2 illustrates a more specific example of the specimen 2, which is aspecimen containing two types of scattered metals, namely, aluminum 21and iron 22, in a resin 20. The characteristic X-rays emitted from thespecimen 2 irradiated with the X-rays from the X-ray source 1 aredetected as a radiation energy spectrum by photon counting performed bythe detector 4, which is, for example, the foregoing semiconductordetector or scintillation detector. The detected spectrum exhibits thepeaks of the aluminum and the iron, as with the one illustrated in FIG.4.

The obtained characteristic X-ray peaks are quantified by a signalprocessor (not illustrated). In the example illustrated in FIG. 2, thepeak intensities of the aluminum 21 and the iron 22 are quantified onthe basis of energy threshold values set in advance to allow thealuminum 21 and the iron 22 to be distinguished from the resin 20 in thespecimen 2. This makes it possible to acquire a transparent image ofonly the aluminum 21 based on the spectrum quantified data between anupper limit value and a lower limit value, and a transparent image ofonly the iron 22 based on the spectrum quantified data which is largerthan the upper limit value. A transparent image of the resin 20 is alsoacquired on the basis of the spectrum quantified data which is smallerthan the lower limit value.

Then, the transparent images obtained as described above are subjectedto reconstruction processing performed by an image reconstruction device(not illustrated), and reconstruction calculation for each energy levelis carried out.

The reconstruction calculation will be further described. If, forexample, the foregoing artifact occurs due to a considerable differencein absorption rate as in the case where metals are scattered in a resin,then the linear attenuation curve of each element of the specimen 2 isdetermined and ideal calculation I=I₀exp^(−t) (μ₁+μ₂+μ₃+ . . . +μ_(n))is carried out. This makes use of the fact that the mass attenuationcoefficient varies according to photon energy. More specifically, asillustrated in FIG. 5, two or more different tube voltages are used,e.g. X-ray sources 1 a and 1 b of tube voltages that are different fromeach other, are used to detect the characteristic X-ray peak of eachelement of the specimen 2 by detectors 4 a and 4 b corresponding to theX-ray sources 1 a and 1 b, respectively. FIG. 6 illustrates the exampleof the linear attenuation coefficient curves of the iron and thealuminum in the case where an X-ray source of 80 kV and an X-ray source1 b of 150 kV are used.

Further, if an artifact occurs because a specimen has a complicatedshape in which the X-ray transmission distance significantly variesdepending on the imaging direction, then the sequential approximatereconstruction method illustrated in FIG. 7 is preferably used.According to the sequential approximate reconstruction method, an actualmeasurement value and an assumed value are compared and a correction ismade each time. An artifact can be removed by repeating the correctionuntil the difference between the actual measurement value and theassumed value falls within an allowable error range set in advance.

It is needless to say that, other than the sequential approximatemethod, various algorithms can be used, such as the method of allpossible combinations (a brute force search), a greedy method, a hillclimbing method, an annealing method, a backpropagation method, agenetic algorithm, genetic programming, an evolution strategy, andevolutionary programming.

Hence, in the image reconstruction, combining the energy sorting by thethreshold value processing or the like and the artifact correction bythe sequential approximate reconstruction or the like makes it possibleto acquire an image from which noises, such as an artifact attributableto a plurality of materials or elements and an artifact attributable toa complicated shape, have been removed.

Although not illustrated, the signal processor and the imagereconstruction device are composed of hardware, such as a computer, andsoftware, such as programs installed in the hardware. More specifically,for example, when a program for carrying out the signal processing andthe image reconstruction processing mentioned above is read into acomputer via a communication medium, such as the Internet, or a memorymedium, such as a USB memory, various types of processing are executedby an arithmetic processing unit, such as a CPU, or a storage unit, suchas a memory. Various types of data required for the execution aresupplied through an input unit or a communication unit, as necessary,and result data is output through an output unit or a display unit.

FIGS. 8A and 8B illustrate a detector, which combines a semiconductordetector and a scintillation detector, as another embodiment of theenergy-dispersive detector. The compound detector illustrated in FIG. 8Ahas a CdTe semiconductor detector, which directly converts X-rays toelectrons, at the X-ray incidence side thereof, and also has ascintillator using CsI, which converts X-rays to light, and a photodiodeor a photomultiplier tube, which uses a semiconductor, such as Ge, Si orthe like, and converts light to electric signals, at the rear sidethereof. The locations of the CdTe semiconductor detector and the Cs1scintillator may be reversed such that X-rays enter and pass through theCs1 scintillator first and then reach the CdTe semiconductor detector.In the compound detector illustrated in FIG. 8B, a semiconductordetector of CdTe or the like, which is capable of detecting an electricsignal on one pixel, and a scintillation detector of Cs1 or the like,which is capable of detecting light, are alternately arranged in achessboard pattern. These arrangements make it possible tosimultaneously acquire sorted energies and X-ray absorption values (CTvalues), thus allowing the entire device to have a simpler configurationand a reduced size.

FIGS. 9A and 9B illustrate an embodiment of a detector adapted to sortenergies by using a filter. In the configuration, a metal filter 50 isprovided in the stage before a CCD camera 5 serving as a detector (referto FIG. 9B; not illustrated in FIG. 9A), and partitions 51 are providedfor individual pixels to prevent rays from scattering. With thisarrangement, as illustrated in FIG. 10, an energy region correspondingto, for example, the resin constituting the specimen 2 (refer to FIG. 2)can be cut off by the metal filter 50 properly selected in advance, sothat only the specimen constituent elements exhibiting high energies,namely, the aluminum and the iron in this example, can be extracted.After the extraction, the reconstruction processing described above iscarried out.

The techniques described above make it possible to image the materialdensity of a region of interest and the characteristics of the texture.An artifact, which has hitherto been a problem, can be eliminated bycorrection, thus allowing a three-dimensional image with higher accuracyto be obtained. Further, the three-dimensional distribution informationon an element contained in a specimen to be measured can be alsoacquired. This is expected to improve the CT measurement technique,achieve an advance in the digital engineering technology, and also to beapplied to the field of high-accuracy simulations.

<Device and Method for X-Ray Three-Dimensional Measurement>

Referring now mainly to FIG. 11 to FIG. 13, the configuration of anX-ray three-dimensional measurement device 10 will be described. Asillustrated in FIG. 11, the X-ray three-dimensional measurement device10 includes an image acquisition device 100 for acquiring an X-ray CTimage of an object to be measured O on a three-dimensional coordinateaxis, an actual measurement device 200 for actually measuring thethree-dimensional shape of the object to be measured O on thethree-dimensional coordinate axis, and an image correction device 300for correcting the X-ray CT image of the object to be measured O whichhas been acquired by the image acquisition device 100, according to thethree-dimensional shape of the object to be measured O which has beenactually measured by the actual measurement device 200.

The image acquisition device 100 irradiates the object to be measured Owith X-rays to detect the projection data for each rotational angle ofthe object to be measured O, thereby acquiring the X-ray CT image of theobject to be measured O on a predetermined three-dimensional coordinateaxis. For this purpose, the image acquisition device 100 has, forexample, an X-ray source 101 that emits X-rays, a detector 102 thatdetects the characteristic X-ray passing through the object to bemeasured O, a mounting table 103 which is disposed between the X-raysource 101 and the detector 102 and on which the object to be measured Ois set, a common stage 104 for installing the X-ray source 101, thedetector 102 and the mounting table 103 thereon, a signal processor 105that quantifies the amount of the characteristic X-ray (the peak of thecharacteristic X-ray) measured by the detector 102, and an imagereconstruction device 106 that reconstructs an image on the basis of thequantified data obtained by the signal processor.

For the detector 102, a flat panel detector, a CdTe detector or the likemay be adopted. The mounting table 103 is configured to rotate about apredetermined rotation axis by a moving mechanism, which is notillustrated, and to linearly move along an axis orthogonal to therotation axis. The mounting table 103 is preferably composed of graniteor a ductile cast iron, which has high stiffness. The center of thethree-dimensional coordinate axis (XYZ axis) used in the imageacquisition device 100 refers to the position of the center of thecommon stage 104 as observed in a planar view and the center is disposedabove the upper surface of the common stage 104 by a predeterminedheight, as illustrated in FIG. 12 and FIG. 13.

The signal processor 105 and the image reconstruction device 106 arecomposed of hardware, such as a computer C, and software, such as aprogram, installed in the hardware. More specifically, when programs forthe signal processor 105 and the image reconstruction device 106 areread into the computer C via a communication medium, such as theInternet, or a memory medium, such as a USB memory, various types ofprocessing are executed by an arithmetic processing unit, such as a CPU,or a storage unit, such as a memory. Various types of data required forthe execution are supplied through an input unit or a communicationunit, as necessary, and result data is output through an output unit ora display unit (e.g. a display screen D).

As with a correction device 302, which will be discussed later, theimage reconstruction device 106 in the present embodiment uses themaximum likelihood estimation and expectation-maximizationreconstruction method (hereinafter referred to as “the ML-EMreconstruction method”) in the sequential approximate reconstructionmethod to reconstruct the X-ray CT image of the object to be measured Oon the basis of the quantified data of the detected amount of theX-rays. The image reconstruction device 106 may reconstruct the image byusing a different algorithm (e.g. a filtered backprojection method, anaddition type ART method, a multiplication type ART method, a SIRTmethod, a gradient method, a steepest descent method, a conjugategradient method, a MAP-EM method, or a convex method).

A linear scale may be disposed between the X-ray source 101 and thedetector 102. This makes it possible to accurately determine theposition of the mounting table 103, so that the X-ray CT image of theobject to be measured O can be accurately acquired.

The actual measurement device 200 is a bridge type device having a probeP, as illustrated in FIG. 12 and FIG. 13, and actually measures thethree-dimensional shape of the object to be measured O on apredetermined three-dimensional coordinate axis. The three-dimensionalcoordinate axis used by the actual measurement device 200 is the same asthe three-dimensional coordinate axis used by the image acquisitiondevice 100.

The three-dimensional coordinate axis (the origin of the probe P) is setautomatically or by an operator so as to establish the positionalrelationship among the object to be measured O, the image acquisitiondevice 100 and the probe P of the actual measurement device 200. Thesetting method may be, for example, the method described inJP2012-137301A, in which a gauge is used to match the central coordinateof a sphere on the X-ray CT image of the gauge and the centralcoordinate of the ball of the gauge measured by the probe P of theactual measurement device 200; however, the setting method is notlimited thereto.

The actual measurement device 200 has a moving mechanism 201, whichrelatively moves the probe P with respect to the object to be measured Oplaced on the mounting table 103. The moving mechanism 201 can becomposed primarily of a cylindrical spindle, which is supported to bevertically movable by a support member and which has the probe P at thedistal end thereof, a Z-direction drive mechanism which moves thespindle in the vertical direction, and an X-direction drive mechanismand a Y-direction drive mechanism which relatively move the mountingtable 103 and the spindle in the directions which are orthogonal to thevertical direction and which are orthogonal to each other. Further, anair balance mechanism which generates, in the spindle, an upward forcebalancing the weight of the spindle including the probe P may be adoptedas a part of the moving mechanism 201 or the actual measurement device200. The probe P and the moving mechanism 201 are installed on thecommon stage 104 on which the X-ray source 101, the detector 102, andthe mounting table 103 of the object to be measured O described aboveare disposed. In other words, the elements for acquiring the X-ray CTimages and the elements for the three-dimensional shape measurement arecombined on the single stage to constitute one measurement device. Thethree-dimensional coordinate axis in the device configuration is set asdescribed above.

Further, the actual measurement device 200 has an input unit 202 whichcan be operated by an operator and a probe moving device 203 which movesthe probe P in response to an operation input through the input unit202. Further, the distal end of the probe P is provided with apressure-sensitive sensor S. When the probe P is moved through the probemoving device 203 in response to an operation performed by the operatorthrough the input unit 202 and comes in contact with the object to bemeasured O, the pressure-sensitive sensor S detects the contact, and thethree-dimensional information of the position of the contact isdetected. The detected three-dimensional position information of theobject to be measured O is sent to the computer C or the like andprocessed. The probe moving device 203 is also composed of hardware,such as the computer C or the like, and software, such as a program,installed in the hardware. When a program for the probe moving device203 is read into the computer C, various types of processing are carriedout by an arithmetic processing unit, such as a CPU, and a storage unit,such as a memory.

The image correction device 300 corrects the X-ray CT image of theobject to be measured O, which has been acquired by the imageacquisition device 100, according to the three-dimensional shape of theobject to be measured O actually measured by the actual measurementdevice 200. As illustrated in FIG. 11, the image correction device 300has a display device 301 which displays, as sinograms, the data of theX-ray CT image acquired by the image acquisition device 100 and the dataof the three-dimensional shape actually measured by the actualmeasurement device 200 on a display screen D, and the correction device302 which reconstructs an image by using the ML-EM reconstruction methodin the sequential approximate reconstruction method such that thesinogram of the X-ray CT image converges to the sinogram of thethree-dimensional shape, thereby correcting the X-ray CT image. Each ofthe display device 301 and the correction device 302 is composed ofhardware, such as the computer C, and software, such as a programinstalled in the hardware. When programs for the display device 301 andthe correction device 302 are read into the computer C, various types ofprocessing are carried out by an arithmetic processing unit, such as aCPU, and a storage unit, such as a memory.

Referring now to FIG. 14 and FIG. 15, the sinograms used for the imagecorrection will be described. FIG. 14 presents explanatory diagrams forexplaining the sinograms of the X-ray CT image of the object to bemeasured O, and FIG. 15 presents explanatory diagrams for explaining thesinograms of the actual measurement data of the three-dimensional shapeof the object to be measured O. The sinogram is an image whichrepresents, in the form of a sine wave, a detection signal for eachangle when the object to be measured O is rotated by 360 degrees, andwhich is acquired for each section of the object to be measured O. Thesinograms of the X-ray CT image (CT sinogram) at a predetermined sectionof the object to be measured O, which has an elliptical shape asobserved in a planar view, acquired by the image acquisition device 100are represented by the images as illustrated in, for example, FIG. 14.Further, the sinograms of the actual measurement data of thethree-dimensional shape (actual measurement sinograms) at apredetermined section of the object to be measured O, which has arectangular shape as observed in a planar view, actually measured by theactual measurement device 200 are represented by the images asillustrated in, for example, FIG. 15. Four sinograms A to D illustratedon the left side in FIG. 15 are the sinograms corresponding to edges Ato D of the object to be measured O illustrated on the right side inFIG. 15. The edges of the object to be measured O are the points ofcontact between the pressure-sensitive sensor S of the probe P of theactual measurement device 200 and the object to be measured O.

Referring now to FIG. 16 and FIG. 17, the ML-EM reconstruction methodused for image correction will be described. The ML-EM reconstructionmethod is a method in which calculation is repeated to determine animage that provides calculated projection data close to the measuredprojection data. It is assumed that projection data (sinograms) at 0°,90°, 180° and 270° has been obtained, as illustrated in FIG. 16. At thistime, the section images that will be obtained from the projection datacan be estimated. For example, it is estimated from the outermostsinogram shape that the external shape is elliptical. Further, thesinograms of 90° and 270° suggest the presence of an extremely brightsubstance at an upper level of the ellipse and also the presence of anair layer at a lower level thereof. The sinograms of 180° and 270°exhibit no information on a substance inside the ellipse, so that it ispresumed that the extremely bright substance and the air layer canceleach other. These procedures are simultaneously repeated to construct aconsistent section image. This has outlined the ML-EM reconstructionmethod.

FIG. 17 illustrates the results of comparison between a section imagereconstructed by using the ML-EM reconstruction method and a sectionimage reconstructed by using the filtered backprojection method(hereinafter referred to as “the FBP method”). The presence ofstreak-like artifacts was observed in the section image reconstructed bythe FBP method. It has also been found that the contrast differs betweenan opening in the specimen and the outer air layer. Meanwhile, suchphenomena have not been observed in the one reconstructed by the ML-EMmethod, but a blurred profile of the opening has been observed. The FBPmethod is an effective reconstruction method for a specimen thatcontains elements having significantly different linear attenuationcoefficients, but less effective for artifacts attributable tocomplicated shapes, such as a plate shape or a shape with manyprojections. This is because the FBP method uses a blur correctionfilter in reconstruction processing. In addition, other problems occur,such as emphasized edges or uneven contrasts, due to the influences of acorrection filter. These problems lead to measurement errors, and themeasurement errors may increase, depending on the shape of an object tobe measured. Meanwhile, the ML-EM reconstruction method is capable ofrestraining the occurrence of artifacts manifested by the FBP method.

However, the ML-EM reconstruction method is a method designed to lead toa statistically most accurate image on the basis of projection data, sothat it has been pointed out that the method poses the following threeproblems: (1) possible failure to converge because the ML-EMreconstruction method is a statistical method; (2) blurry edges ofreconstructed images; and (3) an enormous volume of analysis with aresultant prolonged time required for the reconstruction. There has beena demand for developing a method that solves these problems in order toapply the ML-EM reconstruction method to practical use. We have solvedthe foregoing problems with the ML-EM reconstruction method by obtaininga correct sinogram which is created from the data obtained by actualmeasurement performed by a three-dimensional measurement unit, such asthe actual measurement device 200 in the present embodiment, or anaccurate cross-sectional image created from CAD data. Then, the entireimage is corrected so as to converge to the sinogram.

FIG. 18 is an explanatory diagram for explaining the method forcorrecting an X-ray CT image by using the sinograms of actualmeasurement data, i.e. the actual measurement sinogram, of athree-dimensional shape. The position of the probe P (thepressure-sensitive sensor S) of the actual measurement device 200 can beexpressed by sine waves (sinogram). The X-ray CT image acquired by theimage acquisition device 100 can be also expressed by sine waves(sinogram). In the present embodiment, the three-dimensional coordinateaxis used in the actual measurement device 200 is the same as thethree-dimensional coordinate axis used in the image acquisition device100. This makes it possible to perfectly match the sinogram of the X-rayCT image (CT sinogram) with the sinogram of the actual measurement dataobtained by the actual measurement device 200 (actual measurementsinogram). Thus, the convergence problem and the prolongedreconstruction time problem are solved by using the accurate sinogram ofthe external shape of the object to be measured O actually measured bythe actual measurement device 200 to reconstruct the X-ray CT image bythe ML-EM reconstruction method.

The X-ray three-dimensional measurement device 10 preferably has avibration-proof function as the measures against vibrations fromoutside. Further, the X-ray three-dimensional device 10 is preferablyshielded by a shielding member composed of lead, tungsten or the like,and the temperature and the humidity therein are preferably maintainedconstant by an air conditioner. Thus, when acquiring image informationor the positional information on a three-dimensional shape, theinfluences of an external environment can be suppressed, allowing moreaccurate three-dimensional information to be obtained.

Referring now to the flowchart of FIG. 19 and also referring to FIG. 18as necessary, a description will be given of the method for correctingthe X-ray CT image of the object to be measured O by using the X-raythree-dimensional measurement device 10 according to the presentembodiment.

First, the X-rays are applied to the object to be measured O from theX-ray source 101 of the image acquisition device 100 in order to detectthe projection data at each rotational angle of the object to bemeasured O by the detector 102, thereby acquiring the X-ray CT image ofthe object to be measured O on a predetermined three-dimensionalcoordinate axis (image acquisition step S1). Then, the sinogram of theacquired X-ray CT image of the object to be measured O (the CT sinogram)is displayed on the display screen D by the display device 301, asillustrated in, for example, FIG. 18 (CT sinogram display step S2).

Then, the three-dimensional shape of the object to be measured O on thethree-dimensional coordinate axis is actually measured by the actualmeasurement device 200 (actual measurement step S3). Next, the sinogramof the three-dimensional shape of the actually measured object to bemeasured O (actual measurement sinogram) is displayed on the displayscreen D by the display device 301 as illustrated in, for example, FIG.18 (actual measurement sinogram display step S4). These actualmeasurement step S3 and actual measurement sinogram display step S4 maybe carried out before the image acquisition step S1 and the CT sinogramdisplay step S2.

Then, the image is reconstructed by using the ML-EM reconstructionmethod such that the CT sinogram is converged to the actual measurementsinogram thereby to correct the X-ray CT image (image correction stepS5). At this time, as illustrated in FIG. 18, the image produced bymerging the CT sinogram and the actual measurement sinogram can bedisplayed on the display screen D by the display device 301 toreconstruct the image.

The X-ray three-dimensional measurement device 10 according to theembodiment described above is capable of correcting the X-ray CT imageof the object to be measured O on the predetermined three-dimensionalcoordinate axis by using the actual measurement values of thethree-dimensional shape of the object to be measured O on the samecoordinate axis. At this time, the sinogram of the three-dimensionalshape of the object to be measured O actually measured by the actualmeasurement device 200 (the actual measurement sinogram) is defined asthe correct sinogram, and the image is reconstructed by using the ML-EMreconstruction method such that the sinogram of the X-ray CT image (theCT sinogram) is converged to the correct sinogram thereby to correct theX-ray CT image, thus permitting the time required for the convergence(the time required for the reconstruction) to be shortened. This makesit possible to provide the advantage of the ML-EM reconstruction method(specifically, the advantage that permits reduced artifacts) while atthe same time obviating the disadvantages of the ML-EM reconstructionmethod (specifically, the disadvantage of the statistical method thatmay fail to accomplish convergence, a blurry edge of a reconstructedimage, and an enormous volume of analysis taking prolonged time forreconstruction).

The foregoing embodiments have illustrated the examples in which thecontact type actual measurement device 200 using the probe P is adopted.Alternatively, however, a non-contact type actual measurement deviceusing a laser, a CCD camera or the like may be adopted.

Further, the foregoing embodiments have illustrated the examples inwhich the sinogram of the actual measurement data of thethree-dimensional shape of the object to be measured O, i.e. the actualmeasurement sinogram, is used to correct the X-ray CT image.Alternatively, however, a correct sinogram created using CAD data may beused in place of the actual measurement sinogram to correct the X-ray CTimage. For example, CAD data may be subjected to voxel conversion andcross-section image conversion to create a correct sinogram, and theimage may be reconstructed using the ML-EM reconstruction method suchthat the CT sinogram is converged to the correct sinogram, therebycorrecting the X-ray CT image.

Further, the foregoing embodiments have illustrated the examples inwhich the X-ray CT image is corrected using the ML-EM reconstructionmethod. However, by converging a CT sinogram to an actual measurementsinogram, it is also possible to correct the X-ray CT image by usingother reconstruction methods (e.g. the filtered backprojection method,the addition type ART method, the multiplication type ART method, theSIRT method, the gradient method, the steepest descent method, theconjugate gradient method, the MAP-EM method, and the convex method).

Further, the foregoing embodiments have illustrated the examples inwhich the X-ray CT image of the object to be measured O composed of asingle material is corrected. However, the X-ray CT image of an objectto be measured O composed of a plurality of materials can be alsocorrected at each energy. For example, if the specimen 2 in which twodifferent metals, namely, the aluminum 21 and the iron 22, are scatteredin the resin 20 is chosen as the object to be measured, as illustratedin FIG. 20, then the obtained characteristic X-ray peaks are firstquantified by the signal processor 105. At this time, the peakintensities of the aluminum 21 and the iron 22 are quantified on thebasis of preset energy threshold values that allow the aluminum 21 andthe iron 22 to be distinguished from the resin 20 in the specimen 2.Thus, a transparent image of the aluminum 21 alone based on the spectrumquantified data between an upper limit value and a lower limit value anda transparent image of the iron 22 alone based on the spectrumquantified data that is larger than the upper limit value are acquired.In addition, a transparent image of the resin 20 is also acquired on thebasis of the spectrum quantified data that is smaller than the lowerlimit value. Then, the image reconstruction device 106 carries out thereconstruction processing on each of the obtained transparent images toacquire the X-ray CT image for each energy, thereby obtaining the CTsinograms. Thereafter, the correct sinogram for each energy is createdusing CAD data or the like, and an image is reconstructed by the ML-EMreconstruction method such that the CT sinogram for each energy isconverged to the corresponding correct sinogram thereby to correct theX-ray CT image for each energy.

The present invention is not intended to be limited to the embodimentsdescribed above, and modifications thereof obtained by those skilled inthe art by adding design changes to the embodiments as appropriate areto be embraced in the scope of the present invention insofar as themodifications include the features of the present invention. In otherwords, the elements and the dispositions thereof, the materials, theconditions, the shapes, sizes and the like included in the embodimentsare not limited to the illustrated ones and may be changed asappropriate. Further, the elements provided in the embodiments can becombined as long as the combinations are technically possible, and thecombinations of the elements are to be embraced in the scope of thepresent invention insofar as the combinations of the elements includethe features of the present invention.

REFERENCE SIGNS LIST

-   -   1, 1 a, 1 b X-ray source    -   2 Specimen to be imaged        -   20 Resin        -   21 Aluminum        -   22 Iron    -   3 Drive mechanism    -   4 Energy-dispersive detector        -   40 Sub-detector    -   5 CCD camera        -   50 Metal filter        -   51 Partition    -   10 X-ray three-dimensional measurement device        -   100 Image acquisition device        -   200 Actual measurement device        -   300 Image correction device    -   O Object to be measured    -   S1 Image acquisition step    -   S3 Actual measurement step    -   S5 Image correction step

What is claimed is:
 1. An X-ray three-dimensional measurement devicecomprising: an image acquisition device that acquires an X-ray CT imageof an object to be measured on a three-dimensional coordinate axis; anactual measurement device that actually measures the three-dimensionalshape of the object to be measured on the three-dimensional coordinateaxis; and an image correction device that corrects the X-ray CT imagesuch that a sinogram of the X-ray CT image of the object to be measured,which has been acquired by the image acquisition device, converges to asinogram of the three-dimensional shape of the object to be measuredwhich has been actually measured by the actual measurement device. 2.The X-ray three-dimensional measurement device according to claim 1,wherein the image correction device corrects the X-ray CT image by usinga maximum likelihood estimation and expectation-maximizationreconstruction method.
 3. The X-ray three-dimensional measurement deviceaccording to claim 1, wherein the image correction device corrects theX-ray CT image by using any one of a filtered backprojection method, anaddition type ART method, a multiplication type ART method, a SIRTmethod, a gradient method, a steepest descent method, a conjugategradient method, a MAP-EM method, and a convex method.
 4. An X-raythree-dimensional measurement method comprising: an image acquisitionstep of acquiring an X-ray CT image of an object to be measured on athree-dimensional coordinate axis; an actual measurement step ofactually measuring a three-dimensional shape of the object to bemeasured on the three-dimensional coordinate axis; and an imagecorrection step of correcting the X-ray CT image such that a sinogram ofthe X-ray CT image of the object to be measured, which has been acquiredin the image acquisition step, converges to a sinogram of thethree-dimensional shape of the object to be measured which has beenactually measured in the actual measurement step.
 5. The X-raythree-dimensional measurement method according to claim 4, wherein theX-ray CT image is corrected using a maximum likelihood estimation andexpectation-maximization reconstruction method in the image correctionstep.
 6. The X-ray three-dimensional measurement method according toclaim 4, wherein the X-ray CT image is corrected using any one of afiltered backprojection method, an addition type ART method, amultiplication type ART method, a SIRT method, a gradient method, asteepest descent method, a conjugate gradient method, a MAP-EM method,and a convex method in the image correction step.
 7. An X-raythree-dimensional image correction program that causes a computer tocarry out an image correction step of correcting an X-ray CT image of anobject to be measured which has been acquired on a three-dimensionalcoordinate axis such that a sinogram of the X-ray CT image converges toa sinogram of a three-dimensional shape of the object to be measuredwhich has been actually measured on the three-dimensional coordinateaxis.
 8. The X-ray three-dimensional image correction program accordingto claim 7, wherein the X-ray CT image is corrected using a maximumlikelihood estimation and expectation-maximization reconstruction methodin the image correction step.
 9. The X-ray three-dimensional correctionprogram according to claim 7, wherein the X-ray CT image is correctedusing any one of a filtered backprojection method, an addition type ARTmethod, a multiplication type ART method, a SIRT method, a gradientmethod, a steepest descent method, a conjugate gradient method, a MAP-EMmethod, and a convex method in the image correction step.